Determination of the spectral complex refractive indices of microalgae cells by light reflectance-transmittance measurement

• Spectral optical constants of algae are retrieved by IQPSO algorithm effectively.
• Estimated results of imaginary part are more accurate than those of real part.
• Double-layer inverse model shows higher accuracy than single-layer inverse model.

Two inverse models, namely as single and double-layer inverse models, are developed on the basis of a light scattering measurement technique to determine the spectral complex refractive indices of microalgae from the total hemispherical reflectance and transmittance measured in-situ. Combined with the Mie theory, a direct problem is solved by the finite volume method with the forward simulation of radiative transfer equation under the incidence of a collimated laser. An inverse problem is solved by an improved Quantum-behaved Particle Swarm Optimization (IQPSO) algorithm. The IQPSO algorithm shows a faster convergence speed and a higher accuracy within a smaller number of generations in retrieving the spectral complex refractive indices than the standard Particle Swarm Optimization (PSO) algorithm and the QPSO algorithm. The spectral complex refractive indices of Chlamydomonas reinhardtii at different wavelengths are estimated on the basis of the IQPSO algorithm with the single-layer inverse model. The influence of measurement errors on the inverse results is also investigated. Results indicate that IQPSO is a potential and effective optimal algorithm to estimate the spectral complex refractive indices of microalgae. The estimated results of the imaginary part of the refractive indices demonstrate a higher accuracy than those of the real part, especially with noisy measurement data. To improve the accuracy of single-layer estimated results, a double-layer inverse model is proposed. The investigation reveals that the double-layer inverse model can obtain more accurate results than the single-layer inverse model, especially with random measurement errors, which is more important for directing the experiment of retrieving optical refractive index of microalgae in the further research.